In the 1980s a number of television sitcoms included stories (usually single episodes) in which single men would meet a fatherless boy, get to know him, and decide to adopt, be a "Big Brother", or otherwise care for him.

This was remarkable in a time in society when single-parent adoptions were rare, and men, especially, were considered less-than-ideal (to say the least) as single parents anyway. It seems unlikely that such a story line would be included in sitcoms of the second decade of the XXIst century.
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Boy Meets World (tv series, 1993-2000)

    "Can I Help to Cheer You?", 12 March 1999 

  Eric Matthews (Will Friedle) is paired with Tommy (J.B. Gaynor) in the Big
  Brother program, and the two become quite close, to the point that Eric
  announces he wants to adopt the boy. His family and friends scoff at the
  idea, but Eric goes to the adoption agency anyway, determined to see it 
  through. There he learns that there is a family in California that also
  wants to adopt Tommy, and Eric realises that the California family would
  be much better for Tommy. Tommy pleads with Eric to let him stay. In a
  twist to the usual sitcom story (and an almost direct quote from the 1958 
  Jerry Lewis film, The Geisha Boy), Eric pretends that he no longer cares about 
  Tommy, so that he will go to California and have a real family. Tommy 
  tearfully says that he hates Eric, though he does visit Eric at his house
  before leaving for California. (All has to end well in sitcoms, eh?)

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Family Ties (tv series, 1982-89)

    "I Gotta Be Ming", 23 February 1983 

  Alex P. Keaton (Michael J. Fox) decides to join the Big Brothers
  program, and is assigned to Ming (Eugene Akutagawa). He disappoints
  the boy, however, when his schedule becomes too demanding to allow
  him to spend much time with the boy.

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Happy Days (tv series, 1974-84)

    "Passages", 8 May 1984  

  Near the end of the series (perhaps hoping for a spin-off?), Arthur 
  Fonzarelli, better-known as Fonzie (Henry Winkler) meets Danny (Danny
  Ponce) in the Big Brother program and ultimately decides to adopt him.
  The city's social agencies at first deny his requests, but after
  he and Howard Cunningham (Tom Bosley) persist, The Fonz is able to adopt
  Danny on the same day that Joanie Cunningham (Erin Moran) and 
  Chachi Arcola (Scott Baio) get married.

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Taxi (tv series, 1978-83)

    "Tony and Brian", 8 January 1980 

  Tony Banta (Tony Danza) has befriended orphan Brian Sims (Marc Anthony 
  Danza, Tony Danza's real-life son) and is worried that no-one seems
  interested in adopting him. Tony's friends suggest that he consider
  adopting Brian, and he takes to the idea enthusiastically. Later,
  a rich family expresses an interest in Brian, and, without knowing of
  Tony's intentions, he disappoints Tony by deciding to go with the 
  "real" family. There's more. For the whole story, the 
  "Tony and Brian" episode is available on YouTube.

    "Jim and the Kid", 11 February 1982 

  Tony Banta (Tony Danza) picks up Terry Booth (Tony LaTorre), a 10-year-old
  who can't pay his fare, and brings him into the station, where Louie
  De Palma (Danny DeVito) wants to call the cops and turn him in as a 
  delinquent. Reverend Jim Ignatowski (Christopher Lloyd) decides to take the 
  boy to his apartment and raise him as his own son (despite the fact that
  this is not possible unless it's officially sanctioned by city
  authorities).

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Wind in the Wire (tv special, 1993)
  Randy Travis and company are making a western film out in the wilderness.
  As they are chasing some bad guys on their horses, someone notices that
  someone is firing live ammunition. Randy investigates, and finds the
  culprit is William B. Montgomery (Nicholas Banko), a boy who has run
  away from his foster care home. He explains that he was firing his
  rifle because he thought Randy (and others) were legitimately in
  trouble. Randy takes a shine to the boy -- an older man on the film
  set explains to the director that Randy, himself, was a renegade boy,
  and "it's only natural . . . for him to want to stop some kid from
  making the same mistakes he made." Randy and the boy become
  inseparable, until the boy misbehaves and Randy deals with him sternly,
  and sends the boy away. Later, Randy tries to make up, and at least
  "say his goodbyes", but can't find the boy. The film company
  moves to a new location, where the boy turns up again, having stowed away
  in a horse trailer. Randy decides that he will try to find the boy's
  estranged sister, but if he can't, he promises the boy can live with him.

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