Large amount of lists concatenation

As mentioned by @ScottBoston this is a graph problem, known as connected components, I suggest you used networkx as indicated by @ScottBoston, in case you cannot here is a version without networkx:

from itertools import combinations


def bfs(graph, start):
    visited, queue = set(), [start]
    while queue:
        vertex = queue.pop(0)
        if vertex not in visited:
            visited.add(vertex)
            queue.extend(graph[vertex] - visited)
    return visited


def connected_components(G):
    seen = set()
    for v in G:
        if v not in seen:
            c = set(bfs(G, v))
            yield c
            seen.update(c)


def graph(edge_list):
    result = {}
    for source, target in edge_list:
        result.setdefault(source, set()).add(target)
        result.setdefault(target, set()).add(source)
    return result


def concat(l):
    edges = []
    s = list(map(set, l))
    for i, j in combinations(range(len(s)), r=2):
        if s[i].intersection(s[j]):
            edges.append((i, j))
    G = graph(edges)

    result = []
    unassigned = list(range(len(s)))
    for component in connected_components(G):
        union = set().union(*(s[i] for i in component))
        result.append(sorted(union))
        unassigned = [i for i in unassigned if i not in component]

    result.extend(map(sorted, (s[i] for i in unassigned)))

    return result


print(concat([[1, 2], [3, 4, 5], [0, 4]]))
print(concat([[1], [1, 2], [0, 2]]))
print(concat([[1, 2], [2, 3], [3, 4]]))

Output

[[0, 3, 4, 5], [1, 2]]
[[0, 1, 2]]
[[1, 2, 3, 4]]

You can use networkx library because is a graph theory and connected components problem:

import networkx as nx

l = [[1,2],[3,4,5],[0,4]]
#l = [[1],[1,2],[0,2]]
#l = [[1, 2], [2, 3], [3, 4]]

G = nx.Graph()

#Add nodes to Graph    
G.add_nodes_from(sum(l, []))

#Create edges from list of nodes
q = [[(s[i],s[i+1]) for i in range(len(s)-1)] for s in l]

for i in q:

    #Add edges to Graph
    G.add_edges_from(i)

#Find all connnected components in graph and list nodes for each component
[list(i) for i in nx.connected_components(G)]

Output:

[[1, 2], [0, 3, 4, 5]]

Output if uncomment line 2 and comment line 1:

[[0, 1, 2]]

Likewise for line 3:

[[1, 2, 3, 4]]