Aishiteruze Baby

This is a shojo manga series with an anime adaptation.

Kippei Katakura is a lazy high-school playboy. He returns home one day to find that his sister has charged him with the upbringing of his five year old cousin Yuzuyu. Yuzuyu's mother couldn't stand the stress of raising her as a single parent and (at least temporarily) can't handle being around Yuzuyu. Kippei takes up the task with great gusto, and the series deals with his development as he cares for Yuzuyu.

The series alternates between Yuzuyu at pre-school, Kippei at high school, and their life together at home, and is chock full of heartwarming moments.

This series makes use of the following tropes:

 * Abusive Parents - one plotline deals with this happening to one of Yuzuyu's friends at school.
 * Baka - Kippei's sister calls him this quite a bit
 * Broken Bird - Miki
 * Blue With Shock
 * Character Development
 * Cool Big Sis - Kippei's sister, mostly to Yuzuyu
 * Chick Magnet - Kippei, especially with Yuzuyu in tow. It seems like half the female cast members have a crush on him.
 * Children Raise You - the main premise of the series is to show how much Kippei changes after Yuzuyu comes into his life.
 * Defrosting Ice Queen - Kokoro
 * Father I Want to Marry My Brother
 * Fish Out of Water - Kippei, who is initially unfamiliar with child-rearing
 * Gratuitous English - in the OP
 * Happily Married - Kippei's parents
 * Japanese Sibling Terminology
 * Love Bubbles - used straight a lot, as this is a Shojo series
 * Love Triangle - they don't last very long, however
 * Missing Mom - A major plot point, and the basis of the story.
 * Official Couple - there's little doubt that Kippei and Kokoro will end up together by the first third of the show.
 * Or by the first third of the Title Sequence.
 * Parental Abandonment - Yuzuyu's mother
 * Parent With New Paramour - Kokoro's father
 * Pick On Someone Your Own Size - Kippei's stalker who picks on Yuzuyu out of jealosy
 * Single Woman Seeks Good Man - Kokoro doesn't give in to Kippei's advances until she realizes how good he is with Yuzuyu
 * Slice of Life
 * Spoiled Brat - Marika, at least until she gets some Character Development
 * Squee - In Universe the girls in Kippei's school when Yuzuyu brings him his lunch
 * Stalker With a Crush - Kippei's stalker
 * The Stoic - Satsuki, Kippei's younger brother
 * Those Two Guys - Kokoro's two friends(Aki and Motoki)
 * Third Person Person - Yuzuyu talks like this, as she's only five
 * Transfer Student Uniforms - there's an episode devoted to Yuzuyu having to switch to the new school's uniform