you can create a node at each end of the lines and then connect these nodes. by adjusting the minimum size of node you can improve aesthetics.
(sorry for my google english)
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,positioning,fit,petri,calc,shadows}
\begin{document}
\begin{tikzpicture}[
parent/.style={%
rounded corners,
thick,
draw=red!75,
fill=red!20,
thick,
inner ysep=2pt,
inner xsep=2pt,
minimum width = 4cm,
minimum height = 1.5cm,
align=center
},
child/.style={%
rounded corners,
thick,
draw=blue!90,
fill=blue!35,
thick,
inner ysep=2pt,
inner xsep=2pt,
minimum width = 4cm,
minimum height = 1.5cm,
align=center
},
grandchild/.style={%
rounded corners,
thick,
draw=green!90,
fill=green!35,
thick,
inner ysep=2pt,
inner xsep=2pt,
minimum width = 4cm,
minimum height = 1.5cm,
align=center
},
line/.style={%
semithick,
->,
shorten >=1pt,
>=stealth'
},
call/.style={%
blue,
semithick,
->,
shorten >=1pt,
>=stealth'
},
return/.style={%
red,
semithick,
->,
shorten >=1pt,
>=stealth'
}]
\node[child] (child) {Child};
\node[parent] at (-6,3) (parent 1) {Node 1\\I have manually\\connected this one};
\node[parent] at (0,3) (parent 2) {Node 2\\I have manually\\connected this one};
\node[parent] at (6,3) (parent 3) {Node 3\\I have manually\\connected this one};
\node[parent] at (-6,-3) (grandchild 1) {Node 4\\I have manually\\connected this one};
\node[parent] at (0,-3) (grandchild 2) {Node 5\\I have NOT manually\\connacted this one};
\node[parent] at (6,-3) (grandchild 3) {Node 6\\I have NOT manually\\connacted this one};
%draw three lines from each parent to each child
\draw [line] (parent 1.south east)node[above left](p1){} -- (child.north west)node[below right](c1){};
\draw [line] (parent 2.south)node[above](p2){} -- (child.north)node[below](c2){};
\draw [line] (parent 3.south west)node[above right](p3){} -- (child.north east) node[below left](c3){};
%draw three lines from each parent to each child
\draw [line] (grandchild 1.north east)node[below left,minimum size=2em](p4){} -- (child.south west)node[above right,minimum size=2em](c4){};
\draw [line] (grandchild 2.north)node[below,minimum size=2em](p5){} -- (child.south)node[above,minimum size=2em](c5){};
\draw [line] (grandchild 3.north west)node[below right](p6){} -- (child.south east)node[above left](c6){};
\foreach \nn in{1,2,3,4,5,6}{
\draw [call] (p\nn) to [bend right=15] (c\nn);
\draw [return] (c\nn) to [bend right=15] (p\nn);
}
\end{tikzpicture}
\end{document}!

It might be easier to just use a separate draw command and specify the in=
and out=
angles:

Code:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes,positioning}
\begin{document}
\tikzstyle{data}=[circle,shade,fill=blue!60, draw]
\tikzstyle{operator}=[shape=rectangle, rounded corners, fill=cyan, draw=cyan]
\begin{tikzpicture}
\node[data] (uncurated) {content};
\path node[operator] (schematize) [below = of uncurated.south]{operation}
edge[<-,thick] node[auto]{\tiny flow} (uncurated.south);
\path [->, thick, red] (uncurated.south) edge (schematize.west);
\end{tikzpicture}
\begin{tikzpicture}
\node[data] (uncurated) {content};
\path node[operator] (schematize) [below = of uncurated.south]{operation}
edge[<-,thick] node[auto]{\tiny flow} (uncurated.south);
\path [->, thick, blue] (uncurated.south) edge[out=-145, in=180] (schematize.west);
\end{tikzpicture}
\end{document}
Best Answer
Add
rounded corners
to the path properties. You can control this by setting a value.