Design of skip lists

There are sample implementations of skip lists in many languages:
In C++ here is one reference
In C# here is another reference
In Python here is another reference
The common features across all these implementations are as follows:
1. Each skip list node has a height and a set of neighboring skip list nodes, precisely as many neighboring nodes as its height, some of which may be null.
2. Each skip list node has some piece of data associated with it.
3. Each skip list node has a key to look it up

Skiplist is initialized with the max height of any node.
Head and tail are initialized and attached

Insert operation:
Find where the node goes by comparing keys
If its a duplicate, don't insert, otherwise perform insert
Use a random number to generate a height

Remove operation:
Find the node to be deleted, traverse using available max height to lowest till you reach the node
for each of the levels on the current node, update head and tail forward references and delete the node
if not found return false